A man covers a certain distance by his own car. Had he moved 6 km/hr faster he would have taken 4 hours less. If he had moved 4 km/hr slower, he would have taken 4 hours more. The distance (in km) is

Let's denote the following:

• The original speed of the man as 's' (in km/hr)
• The original time taken to cover the distance as 't' (in hours)
• The distance covered as 'd' (in km)

From the problem, we have two equations based on the relationship between speed, time, and distance:

1. If the man moved 6 km/hr faster, he would have taken 4 hours less. This gives us the equation: d = (s + 6)(t - 4)
2. If the man moved 4 km/hr slower, he would have taken 4 hours more. This gives us the equation: d = (s - 4)(t + 4)

Since both equations are equal to 'd', we can set them equal to each other and solve for 's':

(s + 6)(t - 4) = (s - 4)(t + 4)

Expanding both sides gives:

st - 4s + 6t - 24 = st + 4s - 4t - 16

Solving for 's' gives:

s = (30 + 2t) / 10

Substituting 's' into the first equation gives:

d = [(30 + 2t) / 10 + 6](t - 4)

Solving for 't' gives:

t = 10

Substituting 't' into the equation for 's' gives:

s = (30 + 2*10) / 10 = 5

Finally, substituting 's' and 't' into the equation for 'd' gives:

d = st = 5*10 = 50 km

So, the distance covered by the man is 50 km.

Let's denote the following:

• The original speed of the man as 's' km/hr
• The original time taken to cover the distance as 't' hours
• The distance covered as 'd' km

From the problem, we have two equations based on the conditions given:

1. If he moved 6 km/hr faster, he would have taken 4 hours less. This can be written as: d = (s+6)(t-4)

2. If he moved 4 km/hr slower, he would have taken 4 hours more. This can be written as: d = (s-4)(t+4)

Since both equations are equal to 'd', we can set them equal to each other and solve for 's' and 't':

(s+6)(t-4) = (s-4)(t+4)

Expanding both sides gives:

st - 4s + 6t - 24 = st + 4s - 4t - 16

Solving for 's' gives:

s = (30 + 2t) / 8

Substitute 's' into the equation d = st:

d = t * (30 + 2t) / 8

Solving for 't' gives:

t = 4 hours

Substitute 't' into the equation for 's':

s = (30 + 2*4) / 8 = 8.5 km/hr

Finally, substitute 's' and 't' into the equation for 'd':

d = 8.5 km/hr * 4 hours = 34 km

So, the distance covered is 34 km.